Infinite dimensional Lie groups and representation theory : Washington, DC, USA 17-21 August 2000 / editors, Augustia Banyaga, Joshua A. Leslie, Theirry Robart.

Format:

Book

Contributor:

Banyaga, Augustin.

Leslie, Joshua A. (Joshua Allensworth), 1933-

Robart, Thierry P., 1963-

Language:

English

Subjects (All):

Infinite dimensional Lie algebras--Congresses.

Infinite dimensional Lie algebras.

Infinite groups--Congresses.

Infinite groups.

Infinite-dimensional manifolds--Congresses.

Infinite-dimensional manifolds.

Lie groups--Congresses.

Lie groups.

Physical Description:

1 online resource (174 p.)

Place of Publication:

River Edge, N.J. : World Scientific, c2002.

Language Note:

English

Summary:

This book constitutes the proceedings of the 2000 Howard conference on "Infinite Dimensional Lie Groups in Geometry and Representation Theory". It presents some important recent developments in this area. It opens with a topological characterization of regular groups, treats among other topics the integrability problem of various infinite dimensional Lie algebras, presents substantial contributions to important subjects in modern geometry, and concludes with interesting applications to representation theory. The book should be a new source of inspiration for advanced graduate students and esta

Contents:

Contents; Inheritance Properties for Lipschitz-Metrizable Frolicher Groups; 1 Introduction; 2 Lipschitz-metrizable Frolicher groups; 3 Inheritance properties for Frolicher-Lie groups; References; Around the Exponential Mapping; 1 Fundamentals of ""finite type"" Lie groups; 1.1 Lie's discovery; 1.2 Fundamental theorems; 2 Formal Transformation groups of ""infinite type""; 2.1 Notations; 2.2 The ""exponential catastrophe""; 2.3 Illustration; 3 Regularity & pathologies; 3.1 A canonical concept; 3.2 Apparent pathologies; 3.3 Concept of S-Lie group; 4 Around the exponential rigidity

4.1 Some order4.2 Formal structure theorems; 5 Analytic isotropy transformation groups of ""infinite type""; 5.1 Topology - Notations; 5.2 Integrability; 5.3 Illustration - Technical remarks; References; On a Solution to a Global Inverse Problem with Respect to Certain Generalized Symmetrizable Kac-Moody Algebras; Introduction; 1 Diffeological algebraic structures; 2 On the integrability of some generalized Kac-Moody algebras; References; The Lie Group of Fourier Intergral Operators on Open Manifolds; Introduction; A-COMPACT CASE; 1 The Lie group structure of FIO* (M) on compact manifolds

1.1 What are Fourier integral operators ?1.2 The exact sequence of groups; 1.3 The principal fiber bundle; 1.4 Step 1: Diffoo 0 as ILH Lie group; 1.5 Step 2: (WDOo)* as ILH Lie group; 1.6 Step 3: The local section; 1.7 Step 4: (FIOo)* as topological group; 1.8 Step 5: (FIOok)* as smooth manifold; 1.9 Step 6: (FIOo)* as ILH Lie group; 1.10 Step 7: FIO* as Lie group; B-NON-COMPACT CASE; 2 Diffeomorphisms of NON-COMPACT manifolds; 2.1 Bounded geometry; 2.2 Bounded maps Coo r(M N); 2.3 The bounded diffeomorphism group Diffp T(M); 2.4 Volume preserving and symplectic diffeomorphisms

2.5 Contact transformations of the restricted cotangent bundle T*M3 Pseudodifferential operators and Fourier integral operators on open manifolds; 3.1 Uniform pseudodifferential operators UWDO(M); 3.2 Uniform Fourier integral operators UFIO(M); 3.3 7 steps to the Lie group UFIO; References; On Some Properties of Leibniz Algebroids; 1 Introduction; 2 Graded Leibniz Algebras and Cohomology; 3 Leibniz Algebroids; 3.1 Definition; 3.2 Some examples; 3.3 Characterization of Leibniz Algebroids; 3.4 Generalized Schouten bracket; 3.5 Cartan differential calculus

3.6 Application: the modular class of a Leibniz algebroid3.7 Relationship with the modular class of a Lie algebroid; References; On the Geometry of Locally Conformal Symplectic Manifolds; 1 Introduction and statements of the results; 1.1 Integration of the extended Lee homomorphism; 2 Examples of exact lcs and of lcps manifolds; 3 Proofs of the results; 3.1 Proof of Lemma 1; 3.2 Proof of Proposition 1; 3.3 Proof of Theorem 2 : Part 1; 3.4 Proof of part 3; 3.5 Proof of part 4; 3.6 Proof of part 5; 3.7 Proof of part 2 of Theorem 2; References

Some Properties of Locally Conformal Symplectic Manifolds

Notes:

Description based upon print version of record.

Includes bibliographical references.

ISBN:

9786611929503

9781281929501

1281929506

9789812777089

9812777083